The exit status in your case will always be that of tee and tee seems successful, so you get a zero. You would have to get it before you hand it over to tee. So maybe you are better off to separate both, ie. redirect output in the known way and check the exit status of the command producing and have a look at the written log with tail -f for example.

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13. How do I get the exit code of cmd1 in cmd1|cmd2
First, note that cmd1 exit code could be non-zero and still don't
mean an error. This happens for instance in
cmd | head -1
you might observe a 141 (or 269 with ksh93) exit status of cmd1,
but it's because cmd was interrupted by a SIGPIPE signal when
"head -1" terminated after having read one line.
To know the exit status of the elements of a pipeline
cmd1 | cmd2 | cmd3
a. with zsh:
The exit codes are provided in the pipestatus special array.
cmd1 exit code is in $pipestatus[1], cmd3 exit code in
$pipestatus[3], so that $? is always the same as
$pipestatus[-1].
b. with bash:
The exit codes are provided in the PIPESTATUS special array.
cmd1 exit code is in ${PIPESTATUS[0]}, cmd3 exit code in
${PIPESTATUS[2]}, so that $? is always the same as
${PIPESTATUS: -1}.
c. with any other Bourne like shells
You need to use a trick to pass the exit codes to the main
shell. You can do it using a pipe(2). Instead of running
"cmd1", you run "cmd1; echo $?" and make sure $? makes it way
to the shell.
exec 3>&1
eval `
# now, inside the `...`, fd4 goes to the pipe
# whose other end is read and passed to eval;
# fd1 is the normal standard output preserved
# the line before with exec 3>&1
exec 4>&1 >&3 3>&-
{
cmd1 4>&-; echo "ec1=$?;" >&4
} | {
cmd2 4>&-; echo "ec2=$?;" >&4
} | cmd3
echo "ec3=$?;" >&4
`
d. with a POSIX shell
You can use this function to make it easier:
run() {
j=1
while eval "\${pipestatus_$j+:} false"; do
unset pipestatus_$j
j=$(($j+1))
done
j=1 com= k=1 l=
for a; do
if [ "x$a" = 'x|' ]; then
com="$com { $l "'3>&-
echo "pipestatus_'$j'=$?" >&3
} 4>&- |'
j=$(($j+1)) l=
else
l="$l \"\$$k\""
fi
k=$(($k+1))
done
com="$com $l"' 3>&- >&4 4>&-
echo "pipestatus_'$j'=$?"'
exec 4>&1
eval "$(exec 3>&1; eval "$com")"
exec 4>&-
j=1
while eval "\${pipestatus_$j+:} false"; do
eval "[ \$pipestatus_$j -eq 0 ]" || return 1
j=$(($j+1))
done
return 0
}
use it as:
run cmd1 \| cmd2 \| cmd3
exit codes are in $pipestatus_1, $pipestatus_2, $pipestatus_3
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